In a high magnetic field Bose-Einstein condensation of excitons is just as likely in a bilayer two-dimensional electron-electron system as it is in a bilayer 2D electron-hole gas. If two 2D electron layers, each at half-filling of the lowest Landau level, are sufficiently close together, the ground state of the system possesses interlayer phase coherence. In the limit of zero interlayer tunneling this coherence develops spontaneously at low, but finite, temperatures. The ground state may be viewed as an equilibrium Bose condensate of excitons: electrons in one layer being bound to (conduction band) holes in the other.
Measurements of the tunneling conductance between the layers have shown that when the separation between the layers is brought below a critical value, the tunneling conductance at zero bias grow explosively. Reminiscent of the dc Josephson effect, these observations directly confirm the existence of the anticipated linearly-dispersing Goldstone mode in the system. This mode is a consequence of a spontaneously broken U(1) symmetry in the bilayer system.
Counterflow transport experiments, in which oppositely directed currents are driven through the two layers, have yielded an equally spectacular result: The Hall resistance of the individual layers vanishes as T?0 in the collective phase, in spite of the large magnetic field which is present. This is a compelling indicator that counterflow proceeds via the collective transport of neutral particles; i.e. interlayer excitons. At the same time, the longitudinal resistance in counterflow also vanishes as T?0. This demonstrates that weak dissipation is present at finite temperatures. This suggests that disorder-induced free vortices are present at all temperatures.
This work is supported by the NSF under Grant No. DMR-0242946 and the DOE under Grant No. DE-FG03-99ER45766.